On Gr neisen's equation for thermal expansion

The practical use of Grüneisen's relations as a means of calculating changes in volume from changes in thermal energy is discussed. The relation is often misquoted in an inaccurate and approximate form, and the correct form is described. The methods used for deducing the constants involved are discussed critically, and a simple and accurate method is described. For the cubic metals silver, copper and aluminium there is a very good agreement between the observed and calculated changes in volume between the absolute zero and a temperature of the order 2/3 of the melting point on the absolute scale, whilst for iron there is good agreement up to the temperature at which the magnetic transformation begins. For the hexagonal metals magnesium and zinc, the equation fails at very low temperatures if the substance has a negative coefficient of expansion in one direction (e.g. zinc), but is otherwise fairly satisfactory for the calculation of changes in volume up to a temperature of the order 2/3 of the absolute melting point.